Wavefunction-based　ab-initio　calculations　of　the　electric-dipole　moments　of　4fN-4fN　transitions　of　lanthanide　ions　are　performed　to　extract　the　Atpλ　intensity　parameters.　The　extraction　method　is　an　extension　of　our　earlier　calculations　of　crystal-field　(CF)　parameters　for　lanthanide　ions　in　crystals.　The　CASSCF/RASSI-SO　(Complete-Active-Space　Self-Consistent-Field/Restricted-Active-Space　State-Interaction　Spin-Orbit)　calculations　have　been　carried　out　on　the　chosen　model　system　of　CaF2:　Ce3+　with　an　interstitial　fluoride　ion　(Fi-)　on　z-axis　(Ce3+　ion　occupying　the　C4v　symmetry　site).　In　consideration　of　the　site　symmetry　and　the　coordination　situation　of　Ce3+　ion　at　C4v　site　in　CaF2　as　well　as　the　superposition　model　(SM),　the　calculated　intensity　parameters　for　Ce3+　ion　can　be　classified　into　three　categories,　and　detailed　discussions　are　then　given.　©　2013　Elsevier　B.V.　All　rights　reserved.